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| A Note on Modeling Factors That Create Dynamic Increasing Returns |
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A Note on Modeling Factors That Create Dynamic Increasing Returns By Henry E. Kilpatrick, Jr. and Jean H. P. Paelinck The Institute of Public Policy George Mason University Fairfax, VA 22030 THIS IS A TEXT COPY WHICH HAS LOST A BIT IN TRANSLATION. PLEASE E-MAIL FOR COPY IN WORD FOR WINDOWS Abstract This article, building on the work of W. Brian Arthur and the previous works of the authors and others, discusses factors leading to the generation of dynamic increasing returns, or increasing returns with a time dimension. It discusses twelve likely causal factors and specifies a dynamic method for modeling this theory using these 12 factors in order to perform empirical tests. JEL Numbers: C4, O1 Key words: complexity, dynamic increasing returns, scale economies Modeling Factors That Create Dynamic Increasing Returns Dynamic increasing returns is the phenomena of increasing returns with a time dimension. As Ragnar Frisch (1965) said, "A distinction between momentary and time shaped production coincides almost exactly with the distinction between static and dynamic theories of production." While the notion of increasing returns in goes back at least as far as Alfred Marshall (1920, 1994) in the economics literature and much further in the engineering literature, it is only recently that it has moved from the static to the dynamic world. In 1988, W. Brian Arthur outlined four factors he believed to be primarily responsible for the phenomenon of dynamic increasing returns. In 1989, he published a seminal theoretical article containing a probability model depicting how these circumstances occur. This paper, building on Arthur's work, extends the number of causal factors to twelve, and sets out a method of modeling this theory such that empirical tests that are lacking in the literature may be performed. Increasing returns implies that a doubling of inputs allows the production of more than double the output; the mathematics and graphical analyses may be found in most intermediate and advanced microeconomics texts. Hence, it is more economically efficient than constant returns, at least in the static sense. Factors Responsible for Dynamic Increasing Returns Discussed below are 12 factors that may lead to dynamic increasing returns. Arthur, as noted above, previously named the first 4 factors. Kilpatrick (1998) contains a less refined listing of most of these factors. 1) Production economies. These consist of economies of scale from the large-scale production of a single product and economies of scope from large-scale, multi-product production (mathematically, scale and scope are quite different). Economies of dimension, or engineering economies are considered to be production economies, although technically it might be put in a class of its own. Engineering economies were the first economies formally perceived. 2) Network externalities, or coordination effects. The addition of a member to a network results not only in that member receiving a gain in utility, but in all members currently in the network receiving benefits from the addition of the new member. The utility gains occur up to a level at which it is no longer advantageous for those outside the network to join it (the Internet, the postal system and the telecommunications system are examples of networks), or congestion costs outweigh the benefits received by network members. 3) Learning effects, by which workers are able to improve products or lower production costs over time. R&D, formal education or training, and learning by doing create these learning effects. Learning effects are embodied in human capital, and depreciate over time as physical capital does. 4) Adaptive expectations, whereby the anticipated market dominance of a particular product or service, due to its perceived superiority, creates a self-fulfilling demand for itself. Arthur also describes this as informational increasing returns. This occurs if customers believe everyone else will use a particular product or service and therefore they use it themselves. This undoubtedly helped Microsoft increase its competitive edge over other software, since computer customers who presumed that their customers, suppliers and other associates were going to use it would want to use compatible software. 5) Production standards, which are specified dimensions of production, quality, and/or function that are imposed upon producers of a particular technology (or good or service) by government, trade associations, or other bodies for the purpose of standardization (David and Bunn, 1988). For example, petroleum products such as gasoline and aviation fuel are specified in terms of API gravity, as defined by the American Petroleum Institute an industry trade group, and must be within those specifications to be sold as a specific product. Production standards may or may not negate quality differences in the product among manufacturers. 6) The existence of gateway technologies, which allow the interchangeable use of two or more products or product designs. For example, the MacIntosh and the IBM PC computers (as well as the "clones" of IBM) were, just a few short years ago, incompatible (and a few years before that, the clones of IBM were not 100% compatible with IBM computers). Now the MacIntosh and PC are practically interchangeable due to gateway technologies. 7) Historical path dependence, or the summation of chance occurrences over time. Arthur (1990) calls this "historical accident." There may be some question as to whether path dependence actually causes dynamic returns by itself, but it is not entirely stochastic, since some purposive decisions are made to pick a particular path (but perhaps for entirely different reasons than the production efficiency assumed in earlier literature). 8) Economies of agglomeration, or economies derived from shared spatially referenced inputs whereby benefits to being in a location with other firms increase with the number of firms in a particular location. These are economies of clustering, which include improvements in communication among suppliers, and among those who work for competing interests but who exchange information due to their proximity. 9) Transfer economies, which are transactions economies derived from location networks. These are similar to agglomeration economies, but the emphasis is on trade among the networked parties rather than information and other exchanges made easier by agglomeration or clustering. 10) Technological feedback (or autocatalytic) economies which allow advanced production quality and standards due to the enhanced quality of inputs. That is, makers of inputs to a process supply higher and higher quality inputs, which makes the outputs of higher and higher quality, which creates greater demand for the outputs. This process continuously feeds back into the system. 11) Organizational improvements within firms, industries or economies. This catch-all category includes improvements in internal management structure, better communications between customers and firms, improvements in institutional factors such as property law and enforcement, leadership for regional strategy development and other things that enhance the production process over time. 12) Information agglomeration. These are economies achieved through the use of modern communications technology such as the Internet and World Wide Web, whereby close proximity or clustering is not necessary to achieve economies. Modeling Dynamic Increasing Returns These 12 factors can be specified as a mathematical model of dynamic returns in the following way. Starting from the 12 identified factors (rather than inputs, an important distinction) that contribute to dynamic returns, a transformation (implicit production) function is defined as: f (y, x; y*, q; g) = 0 = f(kly, kx; y*, q; g) (1) with k,l > 1 (economies of scale, factor 1). A multiple output vector is defined as y, x is an input vector, y* an input-output vector of all other activities (externalities and technological feedbacks, or factors 2, 6, 8, 9, 10, 11 and 12), q a consumption vector (externalities again), and g government intervention (production standards, factor 5). Let it be assumed that: yi/xj, yi/y*j, yi/qj, yi/gj > 0 (2) Learning (factor 3), adaptive expectations (factor 4) and historical path dependence (factor 7), supposing now only one global output, are subsumed, together with y*t, qt and gt, under u*t: yt = (gyt-1 + u* t]l (3) (3) is in fact a dynamic generalization of the scale economies specification mentioned earlier. Two possibilities to treat (3) can be envisaged. First take logarithms of (3) and assume provisionally u* t = 0, subtract ln y t-1, and compute the l-effect, which gives : ln yt = l ln gyt-1 (4) so : D ln yt - lnyt-1 = D'ln yt = l ln gyt-1 - lnyt-1 (5) = l ln g + l lnlt-1 - lnlt-1 (6) and finally : D' ln yt = l ln g + (a -1) lnyt-1 (7) of which a crucial test for dynamic returns is the positivity and significance of l - 1, while, as said before, assuming provisionally u*t = 0, or subsuming it under an extra constant plus a stochastic term. Where does dynamic returns complexity as chaotic behavior (see Paelinck, 1998) come in from (7) ? Redefine : D ln lt = z t (8a) and : l ln(1 + g) = b (8b) This allows us to write : zt = b+ lzt-1 (9) Suppose now a negative shock, et , were to occur, such that zt thereafter becomes negative : zt+1 = b + lzt (10) If zt < l-1b, then given that l >1, a positive trend can be reversed. Dynamic returns with complexity will be even more probable if (3) is embedded in a system of similar equations for other firms, again with absorbable shocks. First trials with model (7) already resulted in acceptable estimates for l, but econometric improvements appeared to still be possible. Indeed, starting again from (3), one can transform it into : yt1/l = g yt-1 + u*t (11) the crucial test now being 1/l<1; this model has been applied using the van Gastel-Paelinck elasticity method (van Gastel and Paelinck, 1995) to a 1981-1996 series of total wages in the computer and data processing services sector for Fairfax County, VA (Kilpatrick, Maillat and Paelinck, 1999); the point estimate for 1/l was 1.21, but the interval estimate covered the possibility of dynamic increasing returns. A possible refinement, smoothing the elasticities series, has yet to be applied. Conclusion This paper has extended the list of factors that contribute to dynamic increasing returns and has developed a model for an empirical test of the existence of this phenomenon that requires a minimum amount of data. Dynamic production models that include inputs as well as output would, of course, be more accurate provided reliable data are available. References Arthur, W. B., 1988, Self-reinforcing mechanisms in economics, in: P. W. Anderson, K. J. Arrow, and D. Pines, eds, The economy as an evolving complex system. (Addison Wesley, Reading, MA) 9-27. Arthur, W. B., 1989, Competing technologies, increasing returns, and lock-in by historical events, The Economic Journal 99, 116-31. Arthur, W. B., 1990, 'Silicon valley' locational clusters: when do increasing returns imply monopoly? Mathematical Social Sciences 19, 235-51. Arthur, W. B., 1996, Increasing returns and the new world of business, Harvard Business Review 74, 100-109. David, P. A. and J. A. Bunn, 1988, "The economics of gateway technologies and network evolution," Information Economics and Policy 3, 165-202. Frisch, R., [translated by R. I. Christopherson], 1965, Theory of production (Rand McNally, Chicago). Gastel, M.A.J.J. van and Paelinck, J.H.P., 1995, Computing Box-Cox transform parameters : a new method and its application to spatial econometrics, in: Anselin, L. and Florax, R.J.G.M. (eds), New Directions in spatial econometrics (Springer, Berlin). Kilpatrick, H.E., Jr, Maillat, D. and Paelinck, J.H.P., Rendemenrs croissants dynamiques spatialisés (Spatialised dynamic increasing returns), presented at the annual conference of the ASRDLF (Association de Science Régionale de Langue Française, French Speaking Regional Science Association), Hyères, France, September 1-3, 1999. Kilpatrick, H. E., Jr., 1998, Empirical complexity: a study of dynamic increasing returns in the semiconductor industry, unpublished Ph.D. dissertation. Marshall, A., Correlation of the tendencies to increasing and to diminishing returns, reprinted in James M. Buchanan and Yong J. Yoon, eds, The return to increasing returns. (University of Michigan Press, Ann Arbor, MI). Marshall, A., 1920, Principles of Economics (Macmillan, London). Paelinck, J. H. P., 1998, Controlling complexity in spatial modeling, unpublished paper. Schelling, T. C., 1978, Micromotives and macrobehavior. (W.W. Norton and Company, New York). > |
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